Homotopy theory of schemes
著者
書誌事項
Homotopy theory of schemes
（SMF/AMS texts and monographs, v. 12）（Astérisque, no 256 (1999)）
American Mathematical Society , Société mathématique de France, c2006
- タイトル別名
-
Théorie homotopique des schémas
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注記
Translation of: Théorie homotopique des schémas. Société mathématique de France. c1999
Bibliography: p. 103-104
内容説明・目次
内容説明
In this text, the author presents a general framework for applying the standard methods from homotopy theory to the category of smooth schemes over a reasonable base scheme $k$. He defines the homotopy category $h(\mathcal{E} k)$ of smooth $k$-schemes and shows that it plays the same role for smooth $k$-schemes as the classical homotopy category plays for differentiable varieties. It is shown that certain expected properties are satisfied, for example, concerning the algebraic $K$-theory of those schemes. In this way, advanced methods of algebraic topology become available in modern algebraic geometry.
目次
Introduction The homotopic category Homotopic excision, homotopic purity and projective blow-ups Homotopic classification of vector bundles Appendix A: Review of homotopic algebra Appendix B: Ample families of invertible bundles on a scheme References.
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